1. There are both types of spells in crafting. The Lore spells you are referring to are learned spells and become a part of your decks just like school trained spells. You can also learn recipes for Treasure Cards from different vendors and your school tree.
2. If your character cannot craft something it's because that character doesn't have the crafting level needed. School doesn't matter, you can craft any school's gear with any other school. Certain high level items like shadow wands cannot be traded, but any wizard can craft any item.